We have a tax id that never changes and is assigned to every person at birth. It’s used for tax purposes. There was some opposition against it due to the centralized and permanent nature, so politicians are careful not to openly use it for other purposes. Behind the scenes it is on the way to become a universal id number for most government databases.
Then there is the tax number, which contains a number of the tax office in your region, so if you move you get a new one. Businesses also get them. This was the old system, which is still in use today.
Health insurance and pension have their own number schemes.
For identification with private parties (like banks) you use your id or passport, which have their own numbers. Owning either an id card or a passport is mandatory.